GENERALIZATION OF THE ITERATIVE DISSIPATIVE METHOD FOR MODELING ELECTROMAGNETIC-FIELDS IN NONUNIFORM MEDIA WITH DISPLACEMENT CURRENTS

The iterative dissipative method (IDM) is based on the simple fact that current induced in a conductive medium is in some sense smaller than the external current generating the field. This statement is a theorem based on the energy conservation law of the electromagnetic field. The method has been used to calculate electromagnetic fields in complicated, laterally inhomogeneous media. Examples include electromagnetic induction in a spherical earth model consisting of inhomogeneous oceans and continents, and numerous studies of electromagnetic induction in planar models representing geological regions with inhomogeneous surface and deep conductive and resistive layers. Although the method was originally designed for thin sheet models, it can be used to solve the electromagnetic field equations in a 3-D medium as well. Up to now the IDM has been applied in media and in the frequency range that allows displacement currents to be neglected. It is the purpose of this paper to show that the IDM as well as its faster modification developed by the authors can be used to solve Maxwell's equations in a general 3-D inhomogeneous medium even if the displacement currents can not be neglected. The method imposes no restrictions on the distribution of resistivity, dielectric permittivity, or external sources.